physics - motion
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scalar - measurements
• physical quantities described by magnitude (size) only, such as mass, time or speed • do not depend on direction; they only tell “how much” • fully defined by a numerical value and unit
vector - measurements
• require both magnitude and direction to be fully defined, such as velocity, force or displacement • mathematical or physical quantity possessing both magnitude (size or length) and direction
examples of scalars
time distance volume speed temperature
examples of vectors
position displacement velocity acceleration force momentum
Distance
Total path length in units (scalar quantity)
Displacement Equation
The change in position of the object from the initial position in units (vector quantity) Final position-initial position (with sign)
Gradient Formulas Application in motion graphs
Represents the rate of change between two variables as rise divided by run on a straight line Rise/run or y2-y1/x2-x1 Gradients describe speed on distance-time and acceleration in speed-time graphs
Speed
Measures how fast an object moves, regardless of direction and is a scalar quantity = distance/time
Velocity
Includes both magnitude and direction, making it a vector quantity representing motion precisely = displacement/time
Speed unit conversions
m/s ↔ km/h Multiply by 3.6 to go m/s → km/h Divide by 3.6 to go km/h → m/s
Instantaneous speed
Measures how fast an object moves at a specific moment, unlike average speed over time
average speed/velocity
over a whole journey Average velocity = total displacement ÷ total time Includes direction
Distance-Time Graph Basics
Distance-time graphs plot distance versus time, revealing how far an object travels and its speed through line gradients.
Displacement-Time Graph Insights
Displacement-time graphs show position relative to start, with gradients representing velocity including direction.
Interpreting Graph Gradients
Steeper gradients mean faster speed or velocity; zero gradients indicate the object is stationary.
Curved Lines and Acceleration
Curved lines on distance/displacement-time graphs represent de/acceleration, showing speeding up or slowing down of objects.
Speed-Time Graph Basics
Speed-time graphs plot speed versus time, revealing how far an object travels and its acceleration through line gradients.
Velocity-Time Graph Insights
Velocity-time graphs show velocity over time, with gradients representing acceleration including direction.
velocity-time graph area
the area under a velocity-time graph represents displacement direction must be considered (positive or negative area)
speed-time graph areas
the area under the line of a speed time graph gives us the distance that the object has travelled
Definition and Formula of acceleration
Acceleration measures the rate of velocity change and is calculated as a = (v − u) / t, showing speed variation over time. measured in m/s²
Positive and Negative Acceleration
Positive acceleration means speeding up, while negative acceleration, or deceleration, means slowing down or reversing speed direction.
force
A force is a push or pull acting on an object Measured in Newtons (N) Can change motion (speed, direction, or shape)
Balanced forces
Equal in size, opposite direction No change in motion